how to python loop with conditions

Based on your question, I am assuming that you want just one school name right before the capacity is exceeded. That could be achieved like this:

import pandas as pd
import numpy as np

capacity = 500

s = pd.Series(['School 1','School 2', 'School 3','School 4', 'School 5'])
p = pd.Series(['132', '458', '333', '300', '258'])
d = pd.Series(['1', '2', '3', '4', '5'])
df = pd.DataFrame(np.c_[s,p,d],columns = ['School Name','Population', 'Distance'])

# converting population to integer values
p = p.astype('int')

# placeholder to store school name
school_name = None

for idx, val in enumerate(p):
  # keep assigning school name until capacity is exceeded
  capacity -= val
  if capacity < 0:
      break
  school_name = s[idx]

# add included column     
df['included'] = np.where(df['School Name'] == school_name, df['School Name'], 0)

Then you can print the df to see that it works indeed:

>>> df1
School Name Population Distance    included
0    School 1        132        1    School 1
1    School 2        458        2           0
2    School 3        333        3           0
3    School 4        300        4           0
4    School 5        258        5           0

However, let's say that you want to keep all the schools until the capacity gets exceeded, it is very simply to modify the above program .. just replace the placeholder and the loop like this:

school_names = []    # placeholder will be a list now
for idx, val in enumerate(p):
    capacity -= val
    if capacity < 0:
        break
    school_names.append(s[idx])    # keep adding schools that do not exceed capacity to the list

# Instead of equality, check if school name is in your list
df['included'] = np.where(df['School Name'].isin(school_names), df['School Name'], 0)

Now, if your capacity = 500 and you change the 2nd population such that p = pd.Series(['132', '128', '333', '300', '258']) then both School 1 and School 2 would be included.